Answer :
To simplify the expression \(\left(8^2\right)^6\), we need to use the properties of exponents. Specifically, the property that states \(\left(a^m\right)^n = a^{m \cdot n}\).
Here’s the step-by-step solution:
1. Identify the base and the exponents in the given expression:
- The base is \(8\).
- The inner exponent is \(2\).
- The outer exponent is \(6\).
2. Apply the exponent multiplication rule \(\left(a^m\right)^n = a^{m \cdot n}\):
[tex]\[ \left(8^2\right)^6 = 8^{2 \cdot 6} \][/tex]
3. Multiply the exponents:
[tex]\[ 2 \cdot 6 = 12 \][/tex]
4. Simplify the expression:
[tex]\[ 8^{2 \cdot 6} = 8^{12} \][/tex]
Therefore, the simplified form of \(\left(8^2\right)^6\) is \(8^{12}\).
Thus, the correct answer is:
C. [tex]\(8^{12}\)[/tex]
Here’s the step-by-step solution:
1. Identify the base and the exponents in the given expression:
- The base is \(8\).
- The inner exponent is \(2\).
- The outer exponent is \(6\).
2. Apply the exponent multiplication rule \(\left(a^m\right)^n = a^{m \cdot n}\):
[tex]\[ \left(8^2\right)^6 = 8^{2 \cdot 6} \][/tex]
3. Multiply the exponents:
[tex]\[ 2 \cdot 6 = 12 \][/tex]
4. Simplify the expression:
[tex]\[ 8^{2 \cdot 6} = 8^{12} \][/tex]
Therefore, the simplified form of \(\left(8^2\right)^6\) is \(8^{12}\).
Thus, the correct answer is:
C. [tex]\(8^{12}\)[/tex]
